[petsc-users] calculating eigenvalues for the Stokes equations in 3D

[Patrick Sanan]

"Solve the forward problem" means "solve the Stokes equations".  This terminology is used to contrast with the "inverse problem"  of recovering the parameters of the Stokes equations (viscosity) from the solution (pressure and velocity). 

Here, it sounds like you need to be able to 
1) solve the (discretized) Stokes equations (see Matt's comments)
2) use SLEPc to analyze the operator (in PETSc, a "Mat" object) and extract the eigenvalues.

> Am 29.10.2019 um 13:58 schrieb alex via petsc-users <petsc-users at mcs.anl.gov>:
> 
> Sorry, perhaps I stated my problem a bit inaccurately and that may have caused misunderstanding. In fact, I need to solve the forward problem, i.e. I have to find eigenvalues for the three dimensional Stokes equations, but I don't know how to do it in SLEPc.
>  
> 29.10.2019, 12:05, "Dave May" <dave.mayhem23 at gmail.com>:
>  
>  
> On Tue, 29 Oct 2019 at 08:59, <av-baron at yandex.ru <mailto:av-baron at yandex.ru>> wrote:
> Hi, Dave! Thank you for your assistance. The problem is that I don't have the matrix representation for my problem.
>  
> You will have to explain in more detail if you want further help.
> Explain what "I don't have the matrix representation for my problem" means.
> If you don't have a matrix representation, how do you solve the forward problem??
>  
> Maybe you mean you use a matrix-free (MF) method. That is still a matrix representation of your problem, however the MF representation does not explicitly store the matrix a_{ij} entries in a CSR (or other) format.
>  
>  I've searched on the internet for a solution, but found only some examples of solving 2D eigenvalue problems for the Stokes equations. Maybe you could help me with the matrix representation for the 3D Stokes eigenvalue problem?
> Thank you in advance,
> Alex
>  
> 29.10.2019, 11:16, "Dave May" <dave.mayhem23 at gmail.com <mailto:dave.mayhem23 at gmail.com>>:
>  
>  
> On Tue 29. Oct 2019 at 08:13, alex via petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>> wrote:
> Hello!
> In my project I have to calculate eigenvalues for the three dimensional Stokes equations with Dirichlet boundary conditions. I would like to use SLEPc iterative solver for this purpose, but I'm not quite sure how I should set up the matrices for the solver. I would be grateful if anyone could share a source code for solving this eigenvalue problem.
>  
> I presume your forward model uses petsc. What matrix representation do you use in that code? Why cannot they be used directly with slepc?
>  
> Thanks
> Dave
>  
>  
>  
> Thank you very much! 
> Alex

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